Finite Group Databasebeta

← #7596079

Subgroups — #7596079

Order 512.

1738 conjugacy classes of subgroups.

The subgroup lattice has 909 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59304C211yesmaximal, characteristic
2#59134C211yesmaximal, characteristic, complemented
3#31745C212yesmaximal, complemented
4#31357C212yesmaximal, complemented
5#28979C212yesmaximal, complemented
6#28773C212yesmaximal, complemented
7#27816C211yesmaximal, characteristic, complemented
8#27648C211yesmaximal, characteristic, complemented
9#26443C211yesmaximal, characteristic, complemented
10#26301C211yesmaximal, characteristic, complemented
11#25535C212yesmaximal, complemented
12#25338C211yesmaximal, characteristic, complemented
13#25234C212yesmaximal, complemented
14#24943C212yesmaximal, complemented
15#24816C211yesmaximal, characteristic, complemented
16#24298C211yesmaximal, characteristic, complemented
17#24119C211yesmaximal, characteristic, complemented
18#22962C211yesmaximal, characteristic, complemented
19#22490C211yesmaximal, characteristic, complemented
20#22488C212yesmaximal, complemented
21C4×#465C211yesmaximal, characteristic, complemented
22C8×#121C211yesmaximal, characteristic, complemented
23C2×#1990C211yesmaximal, characteristic, complemented
24C2×#556C2211yescharacteristic
25C2×#553C2212yes—
26C22×C4⋊Q8C2211yescharacteristic
27C2×#484C2212yes—
28C2×#474C2211yescharacteristic
29C2×#474C2211yescharacteristic
30C2×#465C2211yescharacteristic
31C2×C4×SD16C2211yescharacteristic
32C2×C8×D4C2212yes—
33C2×C8×D4C2211yescharacteristic
34C22×C4×C8C2211yescharacteristic
35#2718—22no—
36#2716—22no—
37#2568C2211yescharacteristic
38#2552C2211yescharacteristic
39#2547C2211yescharacteristic
40#2545—21no—
41#2537C2211yescharacteristic
42#2501—21no—
43#2496—21no—
44#2492C2212yes—
45#2487C2212yes—
46#2481—22no—
47#2446—21no—
48#2443—22no—
49#2441C2212yes—
50#2439C2212yes—
51#2436—21no—
52#2422C2212yes—
53#2417C2212yes—
54#2416—21no—
55#2365C2211yescharacteristic
56#2354C2211yescharacteristic
57#2352C2212yes—
58D4×C4⋊C4—21no—
59D4×C4⋊C4C2211yescharacteristic
60Q8×C22⋊C4—21no—
61C4×C22⋊Q8C2211yescharacteristic
62C4×#121C2211yescharacteristic
63C4×#121C2211yescharacteristic
64C2×#384C2211yescharacteristic
65#2101C2212yes—
66#2087C2212yes—
67#2085C2212yes—
68#2083C2212yes—
69#2077C2212yes—
70#2076C2212yes—
71#2075C2212yes—
72#2072C2212yes—
73#2068C2212yes—
74#2059C2212yes—
75#2057C2212yes—
76#2036C2212yes—
77#2033C2212yes—
78#2026C2212yes—
79#2023C2212yes—
80#2000C2212yes—
81#1991C2212yes—
82#1990C2212yes—
83#1990C2212yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1989C2212yes—
89#1988C2211yescharacteristic
90#1988C2211yescharacteristic
91#1968C2211yescharacteristic
92#1954C2211yescharacteristic
93#1947C2211yescharacteristic
94#1947C2211yescharacteristic
95#1942C2212yes—
96#1941C2211yescharacteristic
97#1939C2211yescharacteristic
98#1934C2211yescharacteristic
99#1933C2211yescharacteristic
100#1933C2212yes—
101#1923C2212yes—
102#1919C2212yes—
103#1918C2212yes—
104#1893C2211yescharacteristic
105#1893C2212yes—
106#1892C2211yescharacteristic
107#1892C2212yes—
108#1877C2212yes—
109#1875C2212yes—
110#1874C2212yes—
111#1873C2212yes—
112#1869C2212yes—
113#1862C2212yes—
114#1854C2212yes—
115#1854C2212yes—
116#1852C2212yes—
117#1825C2212yes—
118#1825C2212yes—
119#1824C2212yes—
120#1808C2212yes—
121#1807C2211yescharacteristic
122#1804C2212yes—
123#1803C2211yescharacteristic
124#1803C2211yescharacteristic
125#1797C2211yescharacteristic
126C4×#106C2211yescharacteristic
127C8×C4⋊C4C2211yescharacteristic
128C4×#103C2211yescharacteristic
129C4×#102C2211yescharacteristic
130C4×#102C2212yes—
131C8×C22⋊C4C2212yes—
132#1735C2212yes—
133C2×#340C2212yes—
134C2×#340C2212yes—
135C23×Q8—21no—
136C22×SD16C2311yescharacteristic
137C23×C8C2311yescharacteristic
138C23×C8C2311yescharacteristic
139C23×C8C2312yes—
140#556—24no—
141#556—42no—
142#553—28no—
143#553—44no—
144C2×C4⋊Q8—24no—
145C2×C4⋊Q8—21no—
146C2×C4⋊Q8—21no—
147C2×C4⋊Q8—42no—
148C2×C4⋊Q8C2311yescharacteristic
149C2×C4⋊Q8C2312yes—
150C2×C4⋊Q8C2311yescharacteristic
151C2×#126—22no—
152C2×#126—22no—
153C2×#125C2312yes—
154C2×#124—21no—
155C2×#124—21no—
156C2×#123—22no—
157C2×#123—22no—
158C2×C22⋊Q8C2311yescharacteristic
159C2×C22⋊Q8C2312yes—
160C2×#121—22no—
161C2×#121—21no—
162C2×#121D411yescharacteristic
163C2×#121C2312yes—
164C2×#121C2311yescharacteristic
165C2×C4×Q8—21no—
166C2×C4×Q8—21no—
167C2×C4×Q8C2311yescharacteristic
168C2×C4×D4—21no—
169C2×C4×D4—22no—
170C2×C4×D4C2311yescharacteristic
171C2×C4×D4C2312yes—
172C2×C4×D4C2312yes—
173C2×C4×D4C2311yescharacteristic
174C2×#117C2312yes—
175C2×#117C2312yes—
176C22×C4⋊C4—21no—
177C22×C4⋊C4—21no—
178C22×C4⋊C4—21no—
179C22×C4⋊C4—21no—
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2312yes—
182C22×C42C2311yescharacteristic
183#484—44no—
184#474—24no—
185#474—42no—
186#465—24no—
187C4×SD16—42no—
188C8×D4—42no—
189C8×D4—44no—
190C2×#107C2312yes—
191C2×#107C2312yes—
192C2×#107C2312yes—
193C2×#107C2312yes—
194C2×#106C2311yescharacteristic
195C2×#106C2311yescharacteristic
196C2×#106C2311yescharacteristic
197C2×C4⋊C8C2311yescharacteristic
198C2×C4⋊C8C2311yescharacteristic
199C2×C4⋊C8C2312yes—
200C2×#103C2311yescharacteristic
201C2×#103C2311yescharacteristic
202C2×#103C2312yes—
203C2×#103C2312yes—
204C2×#103C2311yescharacteristic
205C2×#102C2311yescharacteristic
206C2×#102C2312yes—
207C2×#102C2311yescharacteristic
208C2×#102C2311yescharacteristic
209C2×#102C2312yes—
210C2×C22⋊C8C2312yes—
211C2×C22⋊C8C2312yes—
212C2×C22⋊C8C2312yes—
213C2×C22⋊C8C2312yes—
214C2×C4×C8—42no—
215C2×C4×C8C2311yescharacteristic
216C2×C4×C8C2311yescharacteristic
217C2×C4×C8C2311yescharacteristic
218C2×C4×C8C2311yescharacteristic
219C2×C4×C8C2312yes—
220#400—22no—
221#400—22no—
222#400—22no—
223#399—22no—
224#399—22no—
225#398—22no—
226#398—22no—
227#397—22no—
228#397—22no—
229#396—22no—
230#396—22no—
231#396—22no—
232#394—22no—
233#394—22no—
234#393—22no—
235#393—22no—
236#391—21no—
237#391—21no—
238#391—21no—
239#391—21no—
240#391—22no—
241#391—22no—
242#391C2312yes—
243#391C2311yescharacteristic
244#390—21no—
245#390D411yescharacteristic
246#390C2311yescharacteristic
247#389—21no—
248#389—22no—
249#389D411yescharacteristic
250#389C2311yescharacteristic
251#389C2312yes—
252#389C2312yes—
253#389C2311yescharacteristic
254#389C2312yes—
255#388—22no—
256#388—22no—
257#388—22no—
258#388—21no—
259#388D412yes—
260#387—22no—
261#387—21no—
262#387—22no—
263#387—22no—
264#387—22no—
265#386—22no—
266#386—22no—
267#386—22no—
268#386—21no—
269#386D412yes—
270#385—21no—
271#385—22no—
272#385—22no—
273#385—22no—
274#384—21no—
275#384—21no—
276#384—21no—
277#384C2311yescharacteristic
278#384C2311yescharacteristic
279#384C2312yes—
280#382C2312yes—
281#380—21no—
282#380—21no—
283#380—22no—
284#380D411yescharacteristic
285#380C2311yescharacteristic
286#380C2311yescharacteristic
287#380C2312yes—
288#380C2312yes—
289#380C2312yes—
290#380C2312yes—
291C4×C4⋊C4—21no—
292C4×C4⋊C4—21no—
293C4×C4⋊C4C2312yes—
294C4×C4⋊C4C2311yescharacteristic
295C4×C4⋊C4C2311yescharacteristic
296C4×C4⋊C4C2311yescharacteristic
297C4×C22⋊C4—21no—
298C4×C22⋊C4—22no—
299C4×C22⋊C4—21no—
300C4×C22⋊C4C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2312yes—
304#340C2312yes—
305#340C2312yes—
306#340C2312yes—
307#340C2311yescharacteristic
308#340C2311yescharacteristic
309#340C2311yescharacteristic
310#340C2312yes—
311#340C2312yes—
312#340C2312yes—
313#340C2312yes—
314#340C2311yescharacteristic
315#340C2312yes—
316#340C2312yes—
317#340C2311yescharacteristic
318#340C2312yes—
319#340C2312yes—
320#340C2312yes—
321#340C2312yes—
322#340C2311yescharacteristic
323#336C2312yes—
324#336C2312yes—
325#336C2312yes—
326C22×Q8—21no—
327C22×Q8—21no—
328C22×Q8—22no—
329C22×Q8—44no—
330C22×Q8—44no—
331C22×Q8—82no—
332C22×Q8C2411yescharacteristic
333C22×D4—21no—
334C22×D4—22no—
335C22×D4C2×D411yescharacteristic
336C22×D4C2×D412yes—
337C22×D4C2411yescharacteristic
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—21no—
341C23×C4—22no—
342C23×C4C2×D411yescharacteristic
343C23×C4C2×D411yescharacteristic
344C23×C4C2412yes—
345C23×C4C2411yescharacteristic
346C2×SD16—22no—
347C2×SD16—22no—
348C2×SD16—41no—
349C22×C8—22no—
350C22×C8—22no—
351C22×C8—22no—
352C22×C8—22no—
353C22×C8—24no—
354C22×C8—41no—
355C22×C8—41no—
356C22×C8—42no—
357C22×C8—42no—
358C22×C8C2411yescharacteristic
359C22×C8C2412yes—
360C22×C8C2411yescharacteristic
361C22×C8C2412yes—
362C22×C8C2411yescharacteristic
363C22×C8C2411yescharacteristic
364C4⋊Q8—24no—
365C4⋊Q8—22no—
366C4⋊Q8—22no—
367C4⋊Q8—22no—
368C4⋊Q8—42no—
369C4⋊Q8—44no—
370C4⋊Q8—44no—
371C4⋊Q8#4114yes—
372#126—48no—
373#126—48no—
374#125—24no—
375#125—42no—
376#124—44no—
377#124—82no—
378#123—48no—
379#123—84no—
380C22⋊Q8—22no—
381C22⋊Q8—22no—
382C22⋊Q8—24no—
383C22⋊Q8—42no—
384#121—24no—
385#121—22no—
386#121—24no—
387#121—42no—
388#121—48no—
389#121—82no—
390#121#4114yes—
391C4×Q8—22no—
392C4×Q8—22no—
393C4×Q8—44no—
394C4×Q8—82no—
395C4×D4—24no—
396C4×D4—24no—
397C4×D4—24no—
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—22no—
402C4×D4—42no—
403C4×D4—48no—
404C4×D4—44no—
405#117—24no—
406#117—24no—
407#117—42no—
408#117—42no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—24no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—42no—
434C2×C4⋊C4—44no—
435C2×C4⋊C4—82no—
436C2×C4⋊C4—82no—
437C2×C4⋊C4—82no—
438C2×C4⋊C4C2×D411yescharacteristic
439C2×C4⋊C4C2×D411yescharacteristic
440C2×C4⋊C4C2×D412yes—
441C2×C4⋊C4C2×D411yescharacteristic
442C2×C4⋊C4C2412yes—
443C2×C4⋊C4C2412yes—
444C2×C4⋊C4C2412yes—
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2411yescharacteristic
447C2×C4⋊C4C2411yescharacteristic
448C2×C4⋊C4C2411yescharacteristic
449C2×C4⋊C4C2411yescharacteristic
450C2×C4⋊C4C2412yes—
451C2×C4⋊C4C2411yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4C2×D412yes—
469C2×C22⋊C4C2×D412yes—
470C2×C22⋊C4C2×D412yes—
471C2×C22⋊C4C2×D412yes—
472C2×C22⋊C4C2×D412yes—
473C2×C42—22no—
474C2×C42—22no—
475C2×C42—22no—
476C2×C42—22no—
477C2×C42—21no—
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—22no—
481C2×C42C2×D411yescharacteristic
482C2×C42C2×D411yescharacteristic
483C2×C42C2412yes—
484C2×C42C2411yescharacteristic
485C2×C42C2411yescharacteristic
486#107—24no—
487#107—42no—
488#107—42no—
489#107—42no—
490#106—22no—
491#106—22no—
492#106—41no—
493C4⋊C8—22no—
494C4⋊C8—22no—
495C4⋊C8—42no—
496#103—22no—
497#103—22no—
498#103—41no—
499#103—42no—
500#103—42no—
501#102—22no—
502#102—22no—
503#102—24no—
504#102—41no—
505#102—42no—
506C22⋊C8—24no—
507C22⋊C8—24no—
508C22⋊C8—42no—
509C22⋊C8—42no—
510C4×C8—22no—
511C4×C8—22no—
512C4×C8—41no—
513C4×C8—41no—
514C4×C8—42no—
515#95—22no—
516#95—21no—
517#95—22no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—22no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—22no—
526#95—21no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95C2×D412yes—
536#95C2×D412yes—
537#95C2×D412yes—
538C24—21no—
539C24C22×D412yes—
540C24C22×D411yescharacteristic
541C2×Q8—24no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—44no—
549C2×Q8—42no—
550C2×Q8—42no—
551C2×Q8—44no—
552C2×Q8—42no—
553C2×Q8—42no—
554C2×Q8—42no—
555C2×Q8—82no—
556C2×Q8—816no—
557C2×D4—24no—
558C2×D4—24no—
559C2×D4—24no—
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—44no—
572C2×D4—82no—
573C2×D4—82no—
574C2×D4C2×#4112yes—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—82no—
609C22×C4—82no—
610C22×C4—82no—
611C22×C4—82no—
612C22×C4—82no—
613C22×C4#13514yes—
614C22×C4C22×D412yes—
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C2×#4112yes—
623C22×C4H(5,𝔽2)12yes—
624C22×C4C2511yescharacteristic
625SD16—44no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—22no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—21no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—22no—
642C2×C8—44no—
643C2×C8—44no—
644C2×C8—84no—
645C2×C82−1+412yes—
646C2×C82−1+412yes—
647C4⋊C4—24no—
648C4⋊C4—22no—
649C4⋊C4—24no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—22no—
662C4⋊C4—21no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C4⋊C4—44no—
674C4⋊C4—44no—
675C4⋊C4—44no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—44no—
684C4⋊C4—82no—
685C4⋊C4—81no—
686C4⋊C4—81no—
687C4⋊C4—82no—
688C4⋊C4—82no—
689C4⋊C4—82no—
690C4⋊C4C2×#4114yes—
691C4⋊C4C2×#4112yes—
692C22⋊C4—24no—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—44no—
699C22⋊C4—44no—
700C22⋊C4—44no—
701C22⋊C4—44no—
702C22⋊C4—44no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—82no—
710C22⋊C4—82no—
711C22⋊C4—82no—
712C22⋊C4—82no—
713C42—22no—
714C42—22no—
715C42—21no—
716C42—22no—
717C42—21no—
718C42—22no—
719C42—44no—
720C42—44no—
721C42—42no—
722C42—42no—
723C42—42no—
724C42—82no—
725C42C2×#4112yes—
726C42H(5,𝔽2)12yes—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23#54612yes—
746C23C2×#13512yes—
747C23#57812yes—
748C23C23×D411yescharacteristic
749Q8—48no—
750Q8—41no—
751Q8—41no—
752Q8—41no—
753Q8—41no—
754Q8—88no—
755Q8—84no—
756D4—22no—
757D4—22no—
758D4—48no—
759D4—48no—
760D4—41no—
761D4—41no—
762D4—44no—
763D4—164no—
764C2×C4—28no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—28no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—88no—
825C2×C4—84no—
826C2×C4—164no—
827C2×C4—164no—
828C2×C4#54612yes—
829C2×C4#54612yes—
830C2×C4#54612yes—
831C2×C4C2×#13512yes—
832C2×C4C2×#13512yes—
833C2×C4#57612yes—
834C2×C4#57712yes—
835C2×C4C22×#4111yescharacteristic
836C2×C4C22×#4111yescharacteristic
837C2×C4C2×H(5,𝔽2)11yescharacteristic
838C2×C4C2×H(5,𝔽2)11yescharacteristic
839C2×C4C2×2−1+411yescharacteristic
840C2×C4C2×2−1+411yescharacteristic
841C8—22no—
842C8—22no—
843C8—41no—
844C8—42no—
845C8—41no—
846C8—42no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22#330214yes—
868C22C2×#54611yescharacteristic
869C22C2×#54611yescharacteristic
870C22#349911yescharacteristic
871C22C22×#13511yescharacteristic
872C22C2×#57611yescharacteristic
873C22C2×#57711yescharacteristic
874C22C2×#57811yescharacteristic
875C4—22no—
876C4—22no—
877C4—22no—
878C4—22no—
879C4—42no—
880C4—42no—
881C4—44no—
882C4—42no—
883C4—42no—
884C4—81no—
885C4—81no—
886C4—81no—
887C4—81no—
888C4—82no—
889C4—82no—
890C4—81no—
891C4—82no—
892C4—81no—
893C4#329714yes—
894C4#348211yescharacteristic
895C4#352011yescharacteristic
896C4#352211yescharacteristic
897C4#353611yescharacteristic
898C2—24no—
899C2—82no—
900C2—82no—
901C2#5940911yescharacteristic
902C2C2×#329711yescharacteristic
903C2C2×#330211yescharacteristic
904C2#6116811yescharacteristic
905C2#6121511yescharacteristic
906C2#6247011yescharacteristic
907C2#6248811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59304C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #59134C2semidirect
3. #31745C2semidirect
4. #31357C2semidirect
5. #28979C2semidirect
6. #28773C2semidirect
7. #27816C2semidirect
8. #27648C2semidirect
9. #26443C2semidirect
10. #26301C2semidirect
11. #25535C2semidirect
12. #25338C2semidirect
13. #25234C2semidirect
14. #24943C2semidirect
15. #24816C2semidirect
16. #24298C2semidirect
17. #24119C2semidirect
18. #22962C2semidirect
19. #22490C2semidirect
20. #22488C2semidirect
21. C4×#465C2semidirect
22. C8×#121C2semidirect
23. C2×#1990C2semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#593042
#591342
#317452
#313572
#289792
#287732
#278162
#276482
#264432
#263012
#255352
#253382
#252342
#249432
#248162
#242982
#241192
#229622
#224902
#224882
C4×#4652
C8×#1212
C2×#19902